Write the given quantity with its unit and the unit you want.
Pick the equivalent: 1000 between kg, g, mg and mcg or L and mL; 1 kg = 2.2 lb; 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 cup = 240 mL.
Write it as a fraction so that the unwanted unit cancels; for a rate, use one fraction per unit that changes.
Check the direction: a smaller unit gives a bigger number.
Round only the final answer, to the precision the question names.
Dosage calculations
Dose from strength
volume = dose / strength
Weight-based dose
dose = mg/kg × body weight
Tablets
number = dose / tablet strength
Units
1 g = 1000 mg, 1 mg = 1000 mcg
Method
Convert the ordered dose and the stock strength to the same unit.
Use desired over have times quantity: (D/H) × Q.
For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
Estimate first and check that the answer is reasonable.
IV infusion rates
Pump rate
mL/h = volume (mL)/time (h)
Drip rate
drops/min = volume (mL) × drop factor / time (min)
Infusion time
time (h) = volume (mL)/rate (mL/h)
Method
Pump rate in mL/h: volume divided by time in hours.
Drip rate in drops/min: volume × drop factor divided by time in minutes.
For time remaining: volume left divided by the rate.
Round as the question or the equipment requires.
IV fluids & fluid balance
Holliday–Segar per hour
4 mL/kg (first 10 kg) + 2 mL/kg (next 10 kg) + 1 mL/kg (each kg above 20)
Holliday–Segar per day
100 / 50 / 20 mL/kg for the same bands
Fluid balance
intake − output
Ice chips
count as half their volume
Urine output
mL/kg/h = mL / (kg × h)
Infusion time
time (h) = volume left (mL) / rate (mL/h)
Volume infused
mL = rate × time
Pediatric & critical-care dosing
Daily dose
mg/day = mg/kg/day × weight (kg)
Doses per day
number = 24 h / dosing interval (h)
Pounds to kilograms
kg = lb / 2.2
Infusion concentration
units/mL = units in bag / bag volume
Pump rate
mL/h = dose per hour / concentration
Titrated drip
mL/h = mcg/kg/min × kg × 60 / (mcg/mL)
Dose from pump rate
mcg/kg/min = mL/h × (mcg/mL) / (60 × kg)
Units
1 mg = 1000 mcg
Pharmacy calculations
Percentage strength
% w/v = g per 100 mL
Amount in a solution
g = % × mL / 100
Ratio strength
1:X = 1 g in X mL; % = 100 / X
Reconstitution
final volume = diluent + powder volume
Concentration
mg/mL = drug in vial / final volume
Alligation
parts of H = T − L, parts of L = H − T
Water or base
0%
2Practice problems
1.Nursing math & unit conversionsMedium
Practice exercise (made-up values, not clinical guidance). A patient is 4 ft 10 in tall. Using 1 ft = 12 in and 1 in = 2.54 cm, find the height h in centimetres, to the nearest whole centimetre.
4 ft 10 in1 ft = 12 in1 in = 2.54 cm
h = cm
2.Nursing math & unit conversionsHard
Practice exercise (made-up values, not clinical guidance). During a shift a patient takes 3 tsp of cough syrup, 1 cup of tea, 1 fl oz of juice. Using the equivalents given, find the total oral intake V in mL.
1 tsp = 5 mL1 cup = 8 fl oz = 240 mL1 fl oz = 30 mL
V = mL
3.Dosage calculationsMedium
An ampoule of epinephrine (adrenaline) is labelled 1:1000 (1 mg/mL). The prescription is 0.3 mg IM for anaphylaxis. What volume V do you draw up?
1:10000.3 mg
V = mL
4.Dosage calculationsHard
A patient weighs 138.6 lb. The prescription is 5 mg/kg as a single dose, and the stock contains 100 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.
138.6 lb5 mg/kg100 mg/1 mL1 kg = 2.2 lb
V = mL
5.IV infusion ratesMedium
An infusion is ordered at 120 mL/h, but no pump is available. It runs by gravity through a giving set of 20 gtt/mL. Find the drip rate R in drops per minute.
120 mL/h20 gtt/mL
R = gtt/min
6.IV infusion ratesHard
200 mg of a drug is diluted in 100 mL and given by gravity through a set of 20 gtt/mL. The order is 60 mg per hour. Find the drip rate R in drops per minute.
200 mg/100 mL60 mg/h20 gtt/mL
R = gtt/min
7.IV fluids & fluid balanceMedium
Practice exercise (made-up values, not clinical guidance). The record shows a patient's intake and output for one 12-hour shift. The IV infusion ran at the rate shown for the whole shift. Find the fluid balance B = intake − output in mL (a negative answer means a net loss). Count ice chips as half their volume.
Practice exercise (made-up values, not clinical guidance). A 1000 mL bag was started at 08:45 and runs by pump at 100 mL/h. How many mL V are left in the bag at 15:15?
1000 mL100 mL/h08:45 → 15:15
V = mL
9.Pediatric & critical-care dosingMedium
Practice exercise (made-up values, not clinical guidance). A bag contains 20 000 units of heparin in 500 mL. The order is 12 units/kg/h for a patient who weighs 64 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
20 000 units/500 mL12 units/kg/h64 kg
R = mL/h
10.Pediatric & critical-care dosingHard
Practice exercise (made-up values, not clinical guidance). A bag contains dopamine 400 mg in 250 mL. The order is 3 mcg/kg/min for a patient who weighs 65 kg. At what rate R do you set the pump, in mL/h? Round to one decimal place.
400 mg/250 mL3 mcg/kg/min65 kg
R = mL/h
11.Pharmacy calculationsMedium
Practice exercise (made-up values, not clinical guidance). A vial contains oxacillin 2000 mg as a powder. The practice label says to add 11.5 mL of sterile water; the powder adds 1 mL to the volume. What is the concentration C in mg/mL after reconstitution?
2000 mg11.5 mL+1 mL
C = mg/mL
12.Pharmacy calculationsHard
Practice exercise (made-up values, not clinical guidance). You must prepare 750 mL of 30% dextrose by mixing 70% and 10% dextrose. How many mL V of the 10% solution do you need? Round to the nearest whole mL.
70%10%30%750 mL
V = mL
3Solutions
1.Nursing math & unit conversions
Answer: h = 147 cm
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
Height in inches
4·12 + 10 = 58 in
Inches to centimetres
h = 58·2.54 = 147.3 ≈ 147 cm
Answer
h = 147 cm
2.Nursing math & unit conversions
Answer: V = 285 mL
Household measures and weight: nursing exams use rounded equivalents: 1 teaspoon (tsp) = 5 mL, 1 tablespoon (tbsp) = 15 mL = 3 tsp, 1 fluid ounce (fl oz) = 30 mL = 2 tbsp, and 1 cup = 8 fl oz = 240 mL. For weight, 1 kg = 2.2 lb and 1 lb = 16 oz; for length, 1 inch = 2.54 cm. Set the conversion up so that the unit you do not want cancels out.
Each item in mL
3 tsp = 3·5 = 15 mL
1 cup = 1·240 = 240 mL
1 fl oz = 1·30 = 30 mL
Add
V = 15 + 240 + 30 = 285 mL
Answer
V = 285 mL
3.Dosage calculations
Answer: V = 0.3 mL
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Concentration
1:1000 = 1 g/1000 mL = 1 mg/mL
Volume
V = 0.3/1 = 0.3 mL
Answer
V = 0.3 mL
US labels now state mg/mL (1 mg/mL = 1:1000; 0.1 mg/mL = 1:10 000). Never give 1 mg/mL epinephrine IV push.
4.Dosage calculations
Answer: V = 3.2 mL
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Weight in kg
138.6/2.2 = 63 kg
Dose
5·63 = 315 mg
Volume
V = (315/100)·1 = 3.15 ≈ 3.2 mL
Answer
V = 3.2 mL
5.IV infusion rates
Answer: R = 40 gtt/min
Infusion rates: a pump is set in mL/h = volume/time in hours. A gravity drip is counted in drops per minute: gtt/min = volume (mL) × drop factor (gtt/mL)/time (min). The drop factor is printed on the tubing package: macrodrip sets deliver 10, 15 or 20 gtt/mL (blood sets often 10 gtt/mL in the US, 15 in the UK) and microdrip sets 60 gtt/mL. Always use the drop factor the question or package gives.
Millilitres per minute
120/60 = 2 mL/min
Drip rate
R = 2·20 = 40 gtt/min
Answer
R = 40 gtt/min
6.IV infusion rates
Answer: R = 10 gtt/min
Dose-based infusions: concentration = amount of drug in the bag/bag volume. Pump rate (mL/h) = dose per hour/concentration, and dose per hour = mL/h × concentration. Convert per-minute doses to per-hour (× 60) and keep the mass units the same (1 g = 1000 mg, 1 mg = 1000 mcg).
Concentration
200/100 = 2 mg/mL
Volume per hour
60/2 = 30 mL/h
Drip rate
R = 30·20/60 = 10 gtt/min
Answer
R = 10 gtt/min
7.IV fluids & fluid balance
Answer: B = 230 mL
Intake and output: intake counts everything that goes in (oral fluids, IV infusions, IV medications and flushes, tube feeds); ice chips count as half their volume. Output counts urine, drains, vomit and other losses. Balance = total intake − total output; a negative balance is a net loss. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Total intake
oral: 150 + 240 + 120 = 510 mL
ice chips: 200/2 = 100 mL
IV infusion: 80·12 = 960 mL
IV antibiotic: 2·50 = 100 mL
total intake = 1670 mL
Total output
200 + 475 + 400 + 225 + 140 = 1440 mL
Balance
B = 1670 − 1440 = 230 mL
Answer
B = 230 mL
Positive: more fluid went in than came out.
8.IV fluids & fluid balance
Answer: V = 350 mL
Infusion time: time (h) = volume to infuse (mL)/rate (mL/h); use the volume still left in the bag, not the bag size. Volume infused = rate × time. Convert decimal hours to hours and minutes with the fraction × 60 (0.5 h = 30 min, not 50 min). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Elapsed time
08:45 → 15:15 = 6.5 h
Volume infused
100·6.5 = 650 mL
Volume left
V = 1000 − 650 = 350 mL
Answer
V = 350 mL
9.Pediatric & critical-care dosing
Answer: R = 19.2 mL/h
Heparin and insulin infusions: concentration = units in the bag/bag volume (units/mL). Pump rate (mL/h) = units per hour/concentration, and units per hour = mL/h × concentration. For a weight-based order, units/h = units/kg/h × weight first. A bolus volume = units needed/vial strength. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Units per hour
12·64 = 768 units/h
Concentration
20 000/500 = 40 units/mL
Pump rate
R = 768/40 = 19.2 mL/h
Answer
R = 19.2 mL/h
10.Pediatric & critical-care dosing
Answer: R = 7.3 mL/h
Titrated drips: first find the concentration in mcg/mL (mg × 1000/mL). For a weight-based order, mcg/min = mcg/kg/min × weight. Then mL/h = mcg/min × 60/concentration. Working backwards, mcg/kg/min = mL/h × concentration/(60 × weight). The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Concentration
400 mg = 400 000 mcg
400 000/250 = 1600 mcg/mL
Dose per minute and per hour
3·65 = 195 mcg/min
195·60 = 11700 mcg/h
Pump rate
R = 11700/1600 = 7.313 ≈ 7.3 mL/h
Answer
R = 7.3 mL/h
11.Pharmacy calculations
Answer: C = 160 mg/mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Final volume
11.5 + 1 = 12.5 mL
Concentration
C = 2000/12.5 = 160 mg/mL
Answer
C = 160 mg/mL
12.Pharmacy calculations
Answer: V = 500 mL
Alligation: to mix a higher strength H and a lower strength L into a target strength T, take (T − L) parts of H and (H − T) parts of L. The parts are crossed: each stock gets the distance from the target to the other stock. Water or a plain base counts as 0%. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.